A CHARACTERIZATION OF HYPERBOLIC SPACES

Abstract

Let M be a complete spacelike hypersurface in the (n + 1)-dimensional Minkowski space Ln+1. Suppose that every unit speed curve X(s) on M satisfies <X"(s), X"(s)> >= -1/r(2) and there exists a point p is an element of M such that for every unit speed geodesic X(s) of M through the point p, <X"(")(s), "(')(s)> = -1/r(2) holds. Then, we show that up to isometries of Ln+1, M is the hyperbolic space H-n(r).